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If f(x)=5x-12, find a value for $x$ so that $f^{-1}(x)=f(x-1)$.

 May 3, 2022
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First, to find \(f^{-1}(x)\), we replace \(x\) with \(f^{-1}(x)\).

 

\(f(f^{-1}(x)) = 5f^{-1}(x) - 12\\ x = 5f^{-1}(x) - 12\\ f^{-1}(x) = \dfrac{x + 12}5\)

 

Also, what is f(x - 1)? We need to find it as well! Whenever we want to find \(f(\triangle)\), we replace x by \((\triangle)\). In this case, replace x with (x - 1).

 

\(f(x - 1) = 5(x - 1) - 12 = 5x - 17\)

 

Then, the equation is just \(\dfrac{x + 12}5 = 5x - 17\). I believe you can solve the linear equation on your own.

 May 3, 2022

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